Charles Darwin high altitude cooking of potatoes

My guess of what happened was that the potatoes were sitting in an open pot that was not in a rolling boil. I'm going to assume that they went down from the pass and the place where "they took up [their] quarters" was at 11,000ft. This region was then, as it is today, almost destitute of vegetation. Darwin notes in the paragraph just before the potato comment that

The root of a small scrubby plant served as fuel, but it made a miserable fire, and the wind was piercingly cold.

Temperatures in that region average close in the 2 to 4C in March. The poor fuel and the winds make it likely that there was no rolling boil and that while parts of the pot may have been at 89C (the boiling temperature at 11000ft) it is likely that the rest of the pot was not. The poor fuel and the cold and dry wind all contributed to the lower temperatures, not just the air pressure. Bubbles form at the bottom of the pot and rise, so the water appears to be boiling, but it is far from the boiling temperature near the upper walls.

I have experienced this problem using my modern MSR backpacking stove, so I imagine it must have been harder with a camp fire. I got the impression they were not carrying tents. Darwin notes that the next day (after the night of the uncooked potatoes) they found shelter under "some large fragments of rock." This makes it likely that there was no cooking inside some big tent and given the meagerness of their equipment, that the pots had no lids.

Darwin left Chile towards Mendoza on 18 March 1835 not along what are today Route 60 in Chile and Route 7 in Argentina, but up the Yeso Valley. When you cross the border you go through the Piuquenes Pass, which is at 13,235ft. What could be reached within a day's walk in the valley below is 10500ft or higher. So the assumption of 11000ft for where the potatoes where boiled seems reasonable.

Blanching at low temperatures (between 55C and 75C) for a little less than half an hour is a known technique for adding firmness to fruits and vegetables that will later be cooked in some other form (see page 283 of McGhee). Figure 2 in the study of potato blanching by Abu-Ghannam and Crowley, shows that potatoes cooked for an hour at 75C or lower had the same firmness of raw potatoes. As the blanching temperature increases to 90C, the softness of a cooked potato is reached in 30 minutes, with 80C being the approximate transition temperature for going into the cooked state.

The results of Abu-Ghannam and Crowley are in line with some of the sous-vide results I have seen, but not all. My guess is that depending on the balance between starch and cellulose the temperature at which pectin stops holding things together can vary.

Water boils at lower temperatures at higher elevations, but drops only to 80C at 19,000ft:

3353m  11,000ft  89C
4572m  15,000ft  85C
5791m  19,000ft  80C

The temperature anything boils/cooks at changes with pressure

With low pressure (high altitude) water boils at a lower temperature, and starch breaks down at a slightly lower temperature too, but probably not enough to make a huge difference

Mr Darwin was a great and popular writer of the time, but not all his work is "scientific", there is lots of story in there, and maybe this is some of that? I assume he didn't have enough much fuel (a common problem at altitude), and therefore never really got the pot boiling for any length of time. They would have taken much longer to cook (time + temp)

Of course the potatoes could have evolved to become resistant to boiling :-)

11000 feet at the international standard atmosphere makes water boil at 87 degrees. What that means is that if the air pressure at sea level would be 1013 hPa (aka millibars) and +19C then at 11000 ft the water would boil at 87 degrees C.

What this means is that you have to use the density altitude to represent your actual air pressure when calculating the boiling point as this takes into account variations of temperature and local weather formations (ie high and low pressure zones), and moisture content of the air. These variations have a huge impact on air density, for example at 11,000ft elevation where the sea level air pressure equivalent is 1013hPa (ie standard atmosphere) and the temperature is 24C (75F) the density altitude is 14,500ft.

Now Darwin said it was cold, so assuming 0C the density altitude at a standard pressure would have been 12,000ft. A low pressure zone could have made that 13000ft. Either would have made cooking potatoes an iffy proposition.